Separation of nonconvex sets with general augmenting functions

Angelia Nedić; Asuman Ozdaglar

doi:10.1287/moor.1070.0296

Separation of nonconvex sets with general augmenting functions

Angelia Nedić, Asuman Ozdaglar

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we consider two geometric optimization problems that are dual to each other and characterize conditions under which the optimal values of the two problems are equal. This characterization relies on establishing separation results for nonconvex sets using general concave surfaces defined in terms of convex augmenting functions. We prove separation results for augmenting functions that are bounded from below, unbounded augmenting functions, and asymptotic augmenting functions.

Original language	English (US)
Pages (from-to)	587-605
Number of pages	19
Journal	Mathematics of Operations Research
Volume	33
Issue number	3
DOIs	https://doi.org/10.1287/moor.1070.0296
State	Published - Aug 2008
Externally published	Yes

Keywords

Augmenting functions
Recession directions
Separation of nonconvex sets

ASJC Scopus subject areas

Mathematics(all)
Computer Science Applications
Management Science and Operations Research

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10.1287/moor.1070.0296

Cite this

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AB - In this paper, we consider two geometric optimization problems that are dual to each other and characterize conditions under which the optimal values of the two problems are equal. This characterization relies on establishing separation results for nonconvex sets using general concave surfaces defined in terms of convex augmenting functions. We prove separation results for augmenting functions that are bounded from below, unbounded augmenting functions, and asymptotic augmenting functions.

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KW - Recession directions

KW - Separation of nonconvex sets

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Separation of nonconvex sets with general augmenting functions

Abstract

Keywords

ASJC Scopus subject areas

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